Vectors can't be "multiplied" in the same way scalars can. We've already learned about scalar multiples, but how about multiplying two vectors together to get a third?
Your first instinct might be to take vectors a=⎝⎛a1a2a3⎠⎞ and b=⎝⎛b1b2b3⎠⎞ and multiply them together as
While this does technically constitute a mathematical formula, it's not one that has much use in anything below graduate mathematics since it doesn't tell us much useful information about the original vectors. The more common types of vector multiplication involve specific formulas that multiply vector components to produce scalar or vector quantities that will give us a lot of information about a and b. In this section, we'll explore a few different kinds of vector operations with similarities to multiplication.
The first is the scalar product.